Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model

A mechanistic computational framework to investigate the hemodynamic fingerprint of the blood oxygenation level-dependent signal

Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is one of the most used imaging techniques to map brain activity or to obtain clinical information about human cortical vasculature, in both healthy and disease conditions. Nevertheless, BOLD fMRI is an indirect measurement of brain functioning triggered by neurovascular coupling. The origin of the BOLD signal is quite complex, and the signal formation thus depends, among other factors, on the topology of the cortical vasculature and the associated hemodynamic changes. To understand the hemodynamic evolution of the BOLD signal response in humans, it is beneficial to have a computational framework available that virtually resembles the human cortical vasculature, and simulates hemodynamic changes and corresponding MRI signal changes via interactions of intrinsic biophysical and magnetic properties of the tissues. To this end, we have developed a mechanistic computational framework that simulates the hemodynamic fingerprint of the BOLD signal based on a statistically defined, three-dimensional, vascular model that approaches the human cortical vascular architecture. The microvasculature is approximated through a Voronoi tessellation method and the macrovasculature is adapted from two-photon microscopy mice data. Using this computational framework, we simulated hemodynamic changes-cerebral blood flow, cerebral blood volume, and blood oxygen saturation-induced by virtual arterial dilation. Then we computed local magnetic field disturbances generated by the vascular topology and the corresponding blood oxygen saturation changes. This mechanistic computational framework also considers the intrinsic biophysical and magnetic properties of nearby tissue, such as water diffusion and relaxation properties, resulting in a dynamic BOLD signal response. The proposed mechanistic computational framework provides an integrated biophysical model that can offer better insights regarding the spatial and temporal properties of the BOLD signal changes.

External drivers of BOLD signal's non-stationarity

A fundamental challenge in neuroscience is to uncover the principles governing how the brain interacts with the external environment. However, assumptions about external stimuli fundamentally constrain current computational models. We show in silico that unknown external stimulation can produce error in the estimated linear time-invariant dynamical system. To address these limitations, we propose an approach to retrieve the external (unknown) input parameters and demonstrate that the estimated system parameters during external input quiescence uncover spatiotemporal profiles of external inputs over external stimulation periods more accurately. Finally, we unveil the expected (and unexpected) sensory and task-related extra-cortical input profiles using functional magnetic resonance imaging data acquired from 96 subjects (Human Connectome Project) during the resting-state and task scans. This dynamical systems model of the brain offers information on the structure and dimensionality of the BOLD signal's external drivers and shines a light on the likely external sources contributing to the BOLD signal's non-stationarity. Our findings show the role of exogenous inputs in the BOLD dynamics and highlight the importance of accounting for external inputs to unravel the brain's time-varying functional dynamics.

On the intersection between data quality and dynamical modelling of large-scale fMRI signals

Large-scale dynamics of the brain are routinely modelled using systems of nonlinear dynamical equations that describe the evolution of population-level activity, with distinct neural populations often coupled according to an empirically measured structural connectivity matrix. This modelling approach has been used to generate insights into the neural underpinnings of spontaneous brain dynamics, as recorded with techniques such as resting state functional MRI (fMRI). In fMRI, researchers have many degrees of freedom in the way that they can process the data and recent evidence indicates that the choice of pre-processing steps can have a major effect on empirical estimates of functional connectivity. However, the potential influence of such variations on modelling results are seldom considered. Here we show, using three popular whole-brain dynamical models, that different choices during fMRI preprocessing can dramatically affect model fits and interpretations of findings. Critically, we show that the ability of these models to accurately capture patterns in fMRI dynamics is mostly driven by the degree to which they fit global signals rather than interesting sources of coordinated neural dynamics. We show that widespread deflections can arise from simple global synchronisation. We introduce a simple two-parameter model that captures these fluctuations and performs just as well as more complex, multi-parameter biophysical models. From our combined analyses of data and simulations, we describe benchmarks to evaluate model fit and validity. Although most models are not resilient to denoising, we show that relaxing the approximation of homogeneous neural populations by more explicitly modelling inter-regional effective connectivity can improve model accuracy at the expense of increased model complexity. Our results suggest that many complex biophysical models may be fitting relatively trivial properties of the data, and underscore a need for tighter integration between data quality assurance and model development.

Cortical depth-dependent modeling of visual hemodynamic responses

A physiologically based three-dimensional (3D) hemodynamic model is developed to predict the experimentally observed blood oxygen level dependent (BOLD) responses versus the cortical depth induced by visual stimuli. Prior 2D approximations are relaxed in order to analyze 3D blood flow dynamics as a function of cortical depth. Comparison of the predictions with experimental data for evoked stimuli demonstrates that the full 3D model performs at least as well as previous approaches while remaining parsimonious. In particular, the 3D model requires significantly fewer assumptions and model parameters than previous models such that there is no longer need to define depth-specific parameter values for spatial spreading, peak amplitude, and hemodynamic velocity.

Determination of Dynamic Brain Connectivity via Spectral Analysis

Spectral analysis based on neural field theory is used to analyze dynamic connectivity via methods based on the physical eigenmodes that are the building blocks of brain dynamics. These approaches integrate over space instead of averaging over time and thereby greatly reduce or remove the temporal averaging effects, windowing artifacts, and noise at fine spatial scales that have bedeviled the analysis of dynamical functional connectivity (FC). The dependences of FC on dynamics at various timescales, and on windowing, are clarified and the results are demonstrated on simple test cases, demonstrating how modes provide directly interpretable insights that can be related to brain structure and function. It is shown that FC is dynamic even when the brain structure and effective connectivity are fixed, and that the observed patterns of FC are dominated by relatively few eigenmodes. Common artifacts introduced by statistical analyses that do not incorporate the physical nature of the brain are discussed and it is shown that these are avoided by spectral analysis using eigenmodes. Unlike most published artificially discretized “resting state networks” and other statistically-derived patterns, eigenmodes overlap, with every mode extending across the whole brain and every region participating in every mode—just like the vibrations that give rise to notes of a musical instrument. Despite this, modes are independent and do not interact in the linear limit. It is argued that for many purposes the intrinsic limitations of covariance-based FC instead favor the alternative of tracking eigenmode coefficients vs. time, which provide a compact representation that is directly related to biophysical brain dynamics.

Structurally constrained effective brain connectivity

The relationship between structure and function is of interest in many research fields involving the study of complex biological processes. In neuroscience in particular, the fusion of structural and functional data can help to understand the underlying principles of the operational networks in the brain. To address this issue, this paper proposes a constrained autoregressive model leading to a representation of effective connectivity that can be used to better understand how the structure modulates the function. Or simply, it can be used to find novel biomarkers characterizing groups of subjects. In practice, an initial structural connectivity representation is re-weighted to explain the functional co-activations. This is obtained by minimizing the reconstruction error of an autoregressive model constrained by the structural connectivity prior. The model has been designed to also include indirect connections, allowing to split direct and indirect components in the functional connectivity, and it can be used with raw and deconvoluted BOLD signal. The derived representation of dependencies was compared to the well known dynamic causal model, giving results closer to known ground-truth. Further evaluation of the proposed effective network was performed on two typical tasks. In a first experiment the direct functional dependencies were tested on a community detection problem, where the brain was partitioned using the effective networks across multiple subjects. In a second experiment the model was validated in a case-control task, which aimed at differentiating healthy subjects from individuals with autism spectrum disorder. Results showed that using effective connectivity leads to clusters better describing the functional interactions in the community detection task, while maintaining the original structural organization, and obtaining a better discrimination in the case-control classification task.

A Network Architecture for Bidirectional Neurovascular Coupling in Rat Whisker Barrel Cortex

Neurovascular coupling is typically considered as a master-slave relationship between the neurons and the cerebral vessels: the neurons demand energy which the vessels supply in the form of glucose and oxygen. In the recent past, both theoretical and experimental studies have suggested that the neurovascular coupling is a bidirectional system, a loop that includes a feedback signal from the vessels influencing neural firing and plasticity. An integrated model of bidirectionally connected neural network and the vascular network is hence required to understand the relationship between the informational and metabolic aspects of neural dynamics. In this study, we present a computational model of the bidirectional neurovascular system in the whisker barrel cortex and study the effect of such coupling on neural activity and plasticity as manifest in the whisker barrel map formation. In this model, a biologically plausible self-organizing network model of rate coded, dynamic neurons is nourished by a network of vessels modeled using the biophysical properties of blood vessels. The neural layer which is designed to simulate the whisker barrel cortex of rat transmits vasodilatory signals to the vessels. The feedback from the vessels is in the form of available oxygen for oxidative metabolism whose end result is the adenosine triphosphate (ATP) necessary to fuel neural firing. The model captures the effect of the feedback from the vascular network on the neuronal map formation in the whisker barrel model under normal and pathological (Hypoxia and Hypoxia-Ischemia) conditions.

Power spectrum of resting-state blood-oxygen-level-dependent signal

Hemodynamic modeling is used to explore the origin, predict, and analyze the power spectrum of the resting-state blood-oxygen-level-dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI), which has been reported to have a power-law form, i.e., P(f)∝f^{-s}, where P(f) is the power, f is the frequency, and s>0 is the power-law exponent. However, current fMRI experimental paradigms have limited acquisition durations, affecting the spectral resolution of fMRI data at the low-frequency regime. Here, the claimed power-law spectrum is investigated by using a recent hemodynamic model to analytically derive the BOLD power spectrum, with parameters that are related to neurophysiology. The theoretical results show that, for all realistic parameter combinations, the BOLD power spectrum is flat at f≲0.01Hz, has a weak resonance originating from intrinsic oscillations of vasodilatory response, and becomes a power law for high frequencies, all of which is in agreement with an empirical data set that describes the spectrum of one subject and brain region. However, the results are contrary to studies reporting a pure power-law spectrum at f≲0.2Hz. The discrepancy is attributed largely to data averaging employed by current approaches that averages together important properties of the BOLD power spectrum, such as its resonance, that biases the spectrum to only show a power law. Data averaging also reduces the high-frequency power-law exponent relative to individual cases. Overall, this work demonstrates how the model can reproduce BOLD dynamics and further analyze its low-frequency behavior. Moreover, it also uses the model to explain the impact of procedures, such as data averaging, on the reported features of the BOLD power spectrum.

Feasibility of functional magnetic resonance imaging of ocular dominance and orientation preference in primary visual cortex

A recent hemodynamic model is extended and applied to simulate and explore the feasibility of detecting ocular dominance (OD) and orientation preference (OP) columns in primary visual cortex by means of functional magnetic resonance imaging (fMRI). The stimulation entails a short oriented bar stimulus being presented to one eye and mapped to cortical neurons with corresponding OD and OP selectivity. Activated neurons project via patchy connectivity to excite other neurons with similar OP in nearby visual fields located preferentially along the direction of stimulus orientation. The resulting blood oxygen level dependent (BOLD) response is estimated numerically via the model's spatiotemporal hemodynamic response function. The results are then used to explore the feasibility of detecting spatial OD-OP modulation, either directly measuring BOLD or by using Wiener deconvolution to filter the image and estimate the underlying neural activity. The effect of noise is also considered and it is estimated that direct detection can be robust for fMRI resolution of around 0.5 mm, whereas detection with Wiener deconvolution is possible at a broader range from 0.125 mm to 1 mm resolution. The detection of OD-OP features is strongly dependent on hemodynamic parameters, such as low velocity and high damping reduce response spreads and result in less blurring. The short-bar stimulus that gives the most detectable response is found to occur when neural projections are at 45 relative to the edge of local OD boundaries, which provides a constraint on the OD-OP architecture even when it is not fully resolved.

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

A user ready, portable, documented software package, NFTsim, is presented to facilitate numerical simulations of a wide range of brain systems using continuum neural field modeling. NFTsim enables users to simulate key aspects of brain activity at multiple scales. At the microscopic scale, it incorporates characteristics of local interactions between cells, neurotransmitter effects, synaptodendritic delays and feedbacks. At the mesoscopic scale, it incorporates information about medium to large scale axonal ranges of fibers, which are essential to model dissipative wave transmission and to produce synchronous oscillations and associated cross-correlation patterns as observed in local field potential recordings of active tissue. At the scale of the whole brain, NFTsim allows for the inclusion of long range pathways, such as thalamocortical projections, when generating macroscopic activity fields. The multiscale nature of the neural activity produced by NFTsim has the potential to enable the modeling of resulting quantities measurable via various neuroimaging techniques. In this work, we give a comprehensive description of the design and implementation of the software. Due to its modularity and flexibility, NFTsim enables the systematic study of an unlimited number of neural systems with multiple neural populations under a unified framework and allows for direct comparison with analytic and experimental predictions. The code is written in C++ and bundled with Matlab routines for a rapid quantitative analysis and visualization of the outputs. The output of NFTsim is stored in plain text file enabling users to select from a broad range of tools for offline analysis. This software enables a wide and convenient use of powerful physiologically-based neural field approaches to brain modeling. NFTsim is distributed under the Apache 2.0 license.

Characterization of the hemodynamic response function across the majority of human cerebral cortex

A brief (<4 s) period of neural activation evokes a stereotypical sequence of vascular and metabolic events to create the hemodynamic response function (HRF) measured using functional magnetic resonance imaging (fMRI). Linear analysis of fMRI data requires that the HRF be treated as an impulse response, so the character and temporal stability of the HRF are critical issues. Here, a simple audiovisual stimulus combined with a fast-paced task was used to evoke a strong HRF across a majority, ∼77%, of cortex during a single scanning session. High spatiotemporal resolution (2-mm voxels, 1.25-s acquisition time) was used to focus HRF measurements specifically on the gray matter for whole brain. The majority of activated cortex responds with positive HRFs, while ∼27% responds with negative (inverted) HRFs. Spatial patterns of the HRF response amplitudes were found to be similar across subjects. Timing of the initial positive lobe of the HRF was relatively stable across the cortical surface with a mean of 6.1 ± 0.6 s across subjects, yet small but significant timing variations were also evident in specific regions of cortex. The results provide guidance for linear analysis of fMRI data. More importantly, this method provides a means to quantify neurovascular function across most of the brain, with potential clinical utility for the diagnosis of brain pathologies such as traumatic brain injury.

Shock-like haemodynamic responses induced in the primary visual cortex by moving visual stimuli

It is shown that recently discovered haemodynamic waves can form shock-like fronts when driven by stimuli that excite the cortex in a patch that moves faster than the haemodynamic wave velocity. If stimuli are chosen in order to induce shock-like behaviour, the resulting blood oxygen level-dependent (BOLD) response is enhanced, thereby improving the signal to noise ratio of measurements made with functional magnetic resonance imaging. A spatio-temporal haemodynamic model is extended to calculate the BOLD response and determine the main properties of waves induced by moving stimuli. From this, the optimal conditions for stimulating shock-like responses are determined, and ways of inducing these responses in experiments are demonstrated in a pilot study.

Response-mode decomposition of spatio-temporal haemodynamics

The blood oxygen-level dependent (BOLD) response to a neural stimulus is analysed using the transfer function derived from a physiologically based poroelastic model of cortical tissue. The transfer function is decomposed into components that correspond to distinct poles, each related to a response mode with a natural frequency and dispersion relation; together these yield the total BOLD response. The properties of the decomposed components provide a deeper understanding of the nature of the BOLD response, via the components' frequency dependences, spatial and temporal power spectra, and resonances. The transfer function components are then used to separate the BOLD response to a localized impulse stimulus, termed the Green function or spatio-temporal haemodynamic response function, into component responses that are explicitly related to underlying physiological quantities. The analytical results also provide a quantitative tool to calculate the linear BOLD response to an arbitrary neural drive, which is faster to implement than direct Fourier transform methods. The results of this study can be used to interpret functional magnetic resonance imaging data in new ways based on physiology, to enhance deconvolution methods and to design experimental protocols that can selectively enhance or suppress particular responses, to probe specific physiological phenomena.

Clinical Applications of Stochastic Dynamic Models of the Brain, Part I: A Primer

Biological phenomena arise through interactions between an organism's intrinsic dynamics and stochastic forces-random fluctuations due to external inputs, thermal energy, or other exogenous influences. Dynamic processes in the brain derive from neurophysiology and anatomical connectivity; stochastic effects arise through sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random effects can be studied with stochastic dynamic models (SDMs). This article, Part I of a two-part series, offers a primer of SDMs and their application to large-scale neural systems in health and disease. The companion article, Part II, reviews the application of SDMs to brain disorders. SDMs generate a distribution of dynamic states, which (we argue) represent ideal candidates for modeling how the brain represents states of the world. When augmented with variational methods for model inversion, SDMs represent a powerful means of inferring neuronal dynamics from functional neuroimaging data in health and disease. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior.

Eigenmodes of brain activity: Neural field theory predictions and comparison with experiment

Neural field theory of the corticothalamic system is applied to predict and analyze the activity eigenmodes of the bihemispheric brain, focusing particularly on their spatial structure. The eigenmodes of a single brain hemisphere are found to be close analogs of spherical harmonics, which are the natural modes of the sphere. Instead of multiple eigenvalues being equal, as in the spherical case, cortical folding splits them to have distinct values. Inclusion of interhemispheric connections between homologous regions via the corpus callosum leads to further splitting that depends on symmetry or antisymmetry of activity between brain hemispheres, and the strength and sign of the interhemispheric connections. Symmetry properties of the lowest observed eigenmodes strongly constrain the interhemispheric connectivity strengths and unihemispheric mode spectra, and it is predicted that most spontaneous brain activity will be symmetric between hemispheres, consistent with observations. Comparison with the eigenmodes of an experimental anatomical connectivity matrix confirms these results, permits the relative strengths of intrahemispheric and interhemispheric connectivities to be approximately inferred from their eigenvalues, and lays the foundation for further experimental tests. The results are consistent with brain activity being in corticothalamic eigenmodes, rather than discrete "networks" and open the way to new approaches to brain analysis.

Physical Models for Simulation and Reconstruction of Human Tissue Deformation Fields in Dynamic MRI

OBJECTIVE

Medical image registration can be formulated as a tissue deformation problem, where parameter estimation methods are used to obtain the inverse deformation. However, there is limited knowledge about the ability to recover an unknown deformation. The main objective of this study is to estimate the quality of a restored deformation field obtained from image registration of dynamic MR sequences.

METHODS

We investigate the behavior of forward deformation models of various complexities. Further, we study the accuracy of restored inverse deformations generated by image registration.

RESULTS

We found that the choice of 1) heterogeneous tissue parameters and 2) a poroelastic (instead of elastic) model had significant impact on the forward deformation. In the image registration problem, both 1) and 2) were found not to be significant. Here, the presence of image features were dominating the performance. We also found that existing algorithms will align images with high precision while at the same time obtain a deformation field with a relative error of 40%.

CONCLUSION

Image registration can only moderately well restore the true deformation field. Still, estimation of volume changes instead of deformation fields can be fairly accurate and may represent a proxy for variations in tissue characteristics. Volume changes remain essentially unchanged under choice of discretization and the prevalence of pronounced image features.

SIGNIFICANCE

We suggest that image registration of high-contrast MR images has potential to be used as a tool to produce imaging biomarkers sensitive to pathology affecting tissue stiffness.

Investigating Human Neurovascular Coupling Using Functional Neuroimaging: A Critical Review of Dynamic Models

The mechanisms that link a transient neural activity to the corresponding increase of cerebral blood flow (CBF) are termed neurovascular coupling (NVC). They are possibly impaired at early stages of small vessel or neurodegenerative diseases. Investigation of NVC in humans has been made possible with the development of various neuroimaging techniques based on variations of local hemodynamics during neural activity. Specific dynamic models are currently used for interpreting these data that can include biophysical parameters related to NVC. After a brief review of the current knowledge about possible mechanisms acting in NVC we selected seven models with explicit integration of NVC found in the literature. All these models were described using the same procedure. We compared their physiological assumptions, mathematical formalism, and validation. In particular, we pointed out their strong differences in terms of complexity. Finally, we discussed their validity and their potential applications. These models may provide key information to investigate various aspects of NVC in human pathology.

Mechanical restriction of intracortical vessel dilation by brain tissue sculpts the hemodynamic response

Understanding the spatial dynamics of dilation in the cerebral vasculature is essential for deciphering the vascular basis of hemodynamic signals in the brain. We used two-photon microscopy to image neural activity and vascular dynamics in the somatosensory cortex of awake behaving mice during voluntary locomotion. Arterial dilations within the histologically-defined forelimb/hindlimb (FL/HL) representation were larger than arterial dilations in the somatosensory cortex immediately outside the FL/HL representation, demonstrating that the vascular response during natural behaviors was spatially localized. Surprisingly, we found that locomotion drove dilations in surface vessels that were nearly three times the amplitude of intracortical vessel dilations. The smaller dilations of the intracortical arterioles were not due to saturation of dilation. Anatomical imaging revealed that, unlike surface vessels, intracortical vessels were tightly enclosed by brain tissue. A mathematical model showed that mechanical restriction by the brain tissue surrounding intracortical vessels could account for the reduced amplitude of intracortical vessel dilation relative to surface vessels. Thus, under normal conditions, the mechanical properties of the brain may play an important role in sculpting the laminar differences of hemodynamic responses.

Determination of effective brain connectivity from functional connectivity using propagator-based interferometry and neural field theory with application to the corticothalamic system

It is shown how to compute both direct and total effective connection matrices (deCMs and teCMs), which embody the strengths of neural connections between regions, from correlation-based functional CMs using propagator-based interferometry, a method that stems from geophysics and acoustics, coupled with the recent identification of deCMs and teCMs with bare and dressed propagators, respectively. The approach incorporates excitatory and inhibitory connections, multiple structures and populations, and measurement effects. The propagator is found for a generalized scalar wave equation derived from neural field theory, and expressed in terms of neural activity correlations and covariances, and wave damping rates. It is then related to correlation matrices that are commonly used to express functional and effective connectivities in the brain. The results are illustrated in analytically tractable test cases.

Deconvolution of neural dynamics from fMRI data using a spatiotemporal hemodynamic response function

Functional magnetic resonance imaging (fMRI) is a powerful and broadly used means of non-invasively mapping human brain activity. However fMRI is an indirect measure that rests upon a mapping from neuronal activity to the blood oxygen level dependent (BOLD) signal via hemodynamic effects. The quality of estimated neuronal activity hinges on the validity of the hemodynamic model employed. Recent work has demonstrated that the hemodynamic response has non-separable spatiotemporal dynamics, a key property that is not implemented in existing fMRI analysis frameworks. Here both simulated and empirical data are used to demonstrate that using a physiologically based model of the spatiotemporal hemodynamic response function (stHRF) results in a quantitative improvement of the estimated neuronal response relative to unphysical space-time separable forms. To achieve this, an integrated spatial and temporal deconvolution is established using a recently developed stHRF. Simulated data allows the variation of key parameters such as noise and the spatial complexity of the neuronal drive, while knowing the neuronal input. The results demonstrate that the use of a spatiotemporally integrated HRF can avoid "ghost" neuronal responses that can otherwise be falsely inferred. Applying the spatiotemporal deconvolution to high resolution fMRI data allows the recovery of neuronal responses that are consistent with independent electrophysiological measures.

Spatiotemporal hemodynamic response functions derived from physiology

Probing neural activity with functional magnetic resonance imaging (fMRI) relies upon understanding the hemodynamic response to changes in neural activity. Although existing studies have extensively characterized the temporal hemodynamic response, less is understood about the spatial and spatiotemporal hemodynamic responses. This study systematically characterizes the spatiotemporal response by deriving the hemodynamic response due to a short localized neural drive, i.e., the spatiotemporal hemodynamic response function (stHRF) from a physiological model of hemodynamics based on a poroelastic model of cortical tissue. In this study, the model's boundary conditions are clarified and a resulting nonlinear hemodynamic wave equation is derived. From this wave equation, damped linear hemodynamic waves are predicted from the stHRF. The main features of these waves depend on two physiological parameters: wave propagation speed, which depends on mean cortical stiffness, and damping which depends on effective viscosity. Some of these predictions were applied and validated in a companion study (Aquino et al., 2012). The advantages of having such a theory for the stHRF include improving the interpretation of spatiotemporal dynamics in fMRI data; improving estimates of neural activity with fMRI spatiotemporal deconvolution; and enabling wave interactions between hemodynamic waves to be predicted and exploited to improve the signal to noise ratio of fMRI.

Model of the transient neurovascular response based on prompt arterial dilation

Brief neural stimulation results in a stereotypical pattern of vascular and metabolic response that is the basis for popular brain-imaging methods such as functional magnetic resonance imagine. However, the mechanisms of transient oxygen transport and its coupling to cerebral blood flow (CBF) and oxygen metabolism (CMRO2) are poorly understood. Recent experiments show that brief stimulation produces prompt arterial vasodilation rather than venous vasodilation. This work provides a neurovascular response model for brief stimulation based on transient arterial effects using one-dimensional convection-diffusion transport. Hemoglobin oxygen dissociation is included to enable predictions of absolute oxygen concentrations. Arterial CBF response is modeled using a lumped linear flow model, and CMRO2 response is modeled using a gamma function. Using six parameters, the model successfully fit 161/166 measured extravascular oxygen time courses obtained for brief visual stimulation in cat cerebral cortex. Results show how CBF and CMRO2 responses compete to produce the observed features of the hemodynamic response: initial dip, hyperoxic peak, undershoot, and ringing. Predicted CBF and CMRO2 response amplitudes are consistent with experimental measurements. This model provides a powerful framework to quantitatively interpret oxygen transport in the brain; in particular, its intravascular oxygen concentration predictions provide a new model for fMRI responses.

The virtual brain integrates computational modeling and multimodal neuroimaging

Brain function is thought to emerge from the interactions among neuronal populations. Apart from traditional efforts to reproduce brain dynamics from the micro- to macroscopic scales, complementary approaches develop phenomenological models of lower complexity. Such macroscopic models typically generate only a few selected-ideally functionally relevant-aspects of the brain dynamics. Importantly, they often allow an understanding of the underlying mechanisms beyond computational reproduction. Adding detail to these models will widen their ability to reproduce a broader range of dynamic features of the brain. For instance, such models allow for the exploration of consequences of focal and distributed pathological changes in the system, enabling us to identify and develop approaches to counteract those unfavorable processes. Toward this end, The Virtual Brain (TVB) ( www.thevirtualbrain.org ), a neuroinformatics platform with a brain simulator that incorporates a range of neuronal models and dynamics at its core, has been developed. This integrated framework allows the model-based simulation, analysis, and inference of neurophysiological mechanisms over several brain scales that underlie the generation of macroscopic neuroimaging signals. In this article, we describe how TVB works, and we present the first proof of concept.

Hemodynamic traveling waves in human visual cortex

Functional MRI (fMRI) experiments rely on precise characterization of the blood oxygen level dependent (BOLD) signal. As the spatial resolution of fMRI reaches the sub-millimeter range, the need for quantitative modelling of spatiotemporal properties of this hemodynamic signal has become pressing. Here, we find that a detailed physiologically-based model of spatiotemporal BOLD responses predicts traveling waves with velocities and spatial ranges in empirically observable ranges. Two measurable parameters, related to physiology, characterize these waves: wave velocity and damping rate. To test these predictions, high-resolution fMRI data are acquired from subjects viewing discrete visual stimuli. Predictions and experiment show strong agreement, in particular confirming BOLD waves propagating for at least 5–10 mm across the cortical surface at speeds of 2–12 mm s-1. These observations enable fundamentally new approaches to fMRI analysis, crucial for fMRI data acquired at high spatial resolution.

Functional magnetic resonance imaging (fMRI) experiments have advanced our understanding of the structure and function of the human brain. Dynamic changes in the flow and concentration of oxygen in blood are observed experimentally in fMRI data via the blood oxygen level dependent (BOLD) signal. Since neuronal activity induces this hemodynamic response, the BOLD signal provides a noninvasive measure of neuronal activity. Understanding the mechanisms that drive this BOLD response is fundamental for accurately inferring the underlying neuronal activity. The goal of this study is to systematically predict spatiotemporal hemodynamics from a biophysical model, then test these in a high resolution fMRI study of the visual cortex. Using this theory, we predict and empirically confirm the existence of hemodynamic waves in cortex – a striking and novel finding.

Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory

It is shown how to compute effective and functional connection matrices (eCMs and fCMs) from anatomical CMs (aCMs) and corresponding strength-of-connection matrices (sCMs) using propagator methods in which neural interactions play the role of scatterings. This analysis demonstrates how network effects dress the bare propagators (the sCMs) to yield effective propagators (the eCMs) that can be used to compute the covariances customarily used to define fCMs. The results incorporate excitatory and inhibitory connections, multiple structures and populations, asymmetries, time delays, and measurement effects. They can also be postprocessed in the same manner as experimental measurements for direct comparison with data and thereby give insights into the role of coarse-graining, thresholding, and other effects in determining the structure of CMs. The spatiotemporal results show how to generalize CMs to include time delays and how natural network modes give rise to long-range coherence at resonant frequencies. The results are demonstrated using tractable analytic cases via neural field theory of cortical and corticothalamic systems. These also demonstrate close connections between the structure of CMs and proximity to critical points of the system, highlight the importance of indirect links between brain regions and raise the possibility of imaging specific levels of indirect connectivity. Aside from the results presented explicitly here, the expression of the connections among aCMs, sCMs, eCMs, and fCMs in terms of propagators opens the way for propagator theory to be further applied to analysis of connectivity.

An integro-partial differential equation for modeling biofluids flow in fractured biomaterials

A novel mathematical model in the framework of a nonlinear integro-partial differential equation governing biofluids flow in fractured biomaterials is proposed, solved, verified, and evaluated. A semi-analytical solution is derived for the equation, verified by a mass-lumped Galerkin finite element method (FEM), and calibrated with two in vitro experimental datasets. The solution process uses separation of variables and results in explicit expression involving complete and incomplete beta functions. The proposed semi-analytical model shows reasonable agreements with the finite element simulator as well as with two in vitro experimental time series and can be successfully used to simulate biofluids (e.g. water, blood, oil, etc.) flow in natural and synthetic porous biomaterials.